Brown the ground pork and ground beef in a large Dutch oven over medium-high heat.  Break up any clumps with a heavy metal flipper, and continue cooking the meat until almost all of the fat has boiled off.  While the meat is cooking, finely chop the onions and celery.

Turn the heat to medium and add the onions, celery, beef broth, and spices.  Peel and grate the potatoes and stir them into the mixture right away or they will turn a pinkish gray color.

Cover the pot and simmer over low heat for 30 minutes.  Remove the lid and stir, adjusting the seasonings as desired.  Simmer for another 30 minutes, uncovered, until almost all of the liquid has evaporated.  The filling should be thick and moist.

Spoon the mixture into a large, shallow dish and allow the filling to cool to room temperature on the counter, about 1 to 1 ½ hours.

Once the pastry has chilled and the filling has cooled, roll out the pastry on a lightly floured surface to about ⅛ inch thick.  Use it to line a 9-inch, deep-dish pie plate.  Spoon all the filling inside, and brush the lip with beaten egg.

Re-roll the remaining pastry and use it cover the filling, pressing down the edges to seal and trimming off excess pastry with a knife.  Crimp the edges with a fork, then brush the whole pie with beaten egg.  Cut a few vent holes in the lid and decorate with pastry scraps as desired.

Bake at 400 F for about 40-50 minutes, until the pastry is evenly browned.  Cover the edge of the crust with aluminum foil if it's getting too dark.